Super-resolution optical fluctuation imaging (SOFI) provides an elegant way of overcoming the diffraction limit in all three spatial dimensions by computing higher-order cumulants of image sequences of blinking fluorophores acquired with a classical widefield microscope. Previously, three-dimensional (3D) SOFI has been demonstrated by sequential imaging of multiple depth positions. Here we introduce a multiplexed imaging scheme for the simultaneous acquisition of multiple focal planes. Using 3D cross-cumulants, we show that the depth sampling can be increased. The simultaneous acquisition of multiple focal planes significantly reduces the acquisition time and thus the photobleaching. We demonstrate multiplane 3D SOFI by imaging fluorescently labelled cells over an imaged volume of up to 65×65×3.5 μm³ without depth scanning. In particular, we image the 3D network of mitochondria in fixed C2C12 cells immunostained with Alexa 647 fluorophores and the 3D vimentin structure in living Hela cells expressing the fluorescent protein Dreiklang.